The symmetric tensor product on the Drinfeld centre of a symmetric fusion category
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The symmetric tensor product on the Drinfeld centre of a symmetric fusion category. / Wasserman, Thomas A.
In: Journal of Pure and Applied Algebra, Vol. 224, No. 8, 106348, 2020.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The symmetric tensor product on the Drinfeld centre of a symmetric fusion category
AU - Wasserman, Thomas A.
PY - 2020
Y1 - 2020
N2 - We define a symmetric tensor product on the Drinfeld centre of a symmetric fusion category, in addition to its usual tensor product. We examine what this tensor product looks like under Tannaka duality, identifying the symmetric fusion category with the representation category of a finite (super)-group. Under this identification, the Drinfeld centre is the category of equivariant vector bundles over the finite group (underlying the super-group, in the super case). In the non-super case, we show that the symmetric tensor product corresponds to the fibrewise tensor product of these vector bundles. In the super case, we define for each super-group structure on the finite group a super-version of the fibrewise tensor product. We show that the symmetric tensor product on the Drinfeld centre of the representation category of the resulting finite super-groups corresponds to this super-version of the fibrewise tensor product on the category of equivariant vector bundles over the finite group.
AB - We define a symmetric tensor product on the Drinfeld centre of a symmetric fusion category, in addition to its usual tensor product. We examine what this tensor product looks like under Tannaka duality, identifying the symmetric fusion category with the representation category of a finite (super)-group. Under this identification, the Drinfeld centre is the category of equivariant vector bundles over the finite group (underlying the super-group, in the super case). In the non-super case, we show that the symmetric tensor product corresponds to the fibrewise tensor product of these vector bundles. In the super case, we define for each super-group structure on the finite group a super-version of the fibrewise tensor product. We show that the symmetric tensor product on the Drinfeld centre of the representation category of the resulting finite super-groups corresponds to this super-version of the fibrewise tensor product on the category of equivariant vector bundles over the finite group.
KW - Drinfeld centre
KW - Fusion categories
UR - http://www.scopus.com/inward/record.url?scp=85080044991&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2020.106348
DO - 10.1016/j.jpaa.2020.106348
M3 - Journal article
AN - SCOPUS:85080044991
VL - 224
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 8
M1 - 106348
ER -
ID: 260678015